The Mirror reports that the incident happened on Friday afternoon when an altercation in a practice match spiralled out of control.
The mother of a Swansea youth team player who was on site at the time is believed to have phoned the police when she saw Chico, 26, screaming at Monk, 34, with a brick in his hand.
Officers at the scene took no action, opting to leave disciplinary matters in the hands of the club, where - the same source claims - there is a growing divide between the Spanish imports and homegrown players.
Swansea's English and Welsh contingent are reportedly becoming frustrated by Chico's dramatic antics, the latest of which was him walking out of a team meeting earlier this week.
A club statement read: "Chico Flores and Garry Monk had an exchange of words, which is not uncommon between players in training grounds across the country, but no threats or altercations took place between the players in question.
"It's understood a member of the public phoned the police, who felt no action was required. The matter has been dealt with and is concluded."
A statement from South Wales Police said: "Police were called to the training ground at around 1.30pm on Friday. Club officials were spoken to and no police action was required."
Chico joined the Swans from Serie A side Genoa for £2m in the summer transfer window of 2012.